Question

complete the proof that ( \triangle hjk cong \triangle jhi ).

Explanation:

Step1: Identify the given congruent sides

From the diagram, we can see that \( \overline{JK}\cong\overline{HI}\) (given as marked in the figure), \( \overline{HK}\cong\overline{IJ}\) (given as marked in the figure).

Step2: Use the reflexive property

For \( \overline{HJ}\cong\overline{HJ}\), by the reflexive property of congruence (a segment is congruent to itself).

Step3: Apply SSS (Side - Side - Side) congruence criterion

Since we have three pairs of congruent sides (\( \overline{JK}\cong\overline{HI}\), \( \overline{HK}\cong\overline{IJ}\), \( \overline{HJ}\cong\overline{HJ}\)), by the SSS congruence criterion, \( \triangle HJK\cong\triangle JHI\).

Answer:

1. Given
2. Given
3. Reflexive Property of Congruence
4. SSS (Side - Side - Side) Congruence Criterion